Question: If y = |3x−5| / (−x^2−3) for what value of x will the value of y be greatest?

1. -5
2. -3/5
3. 0
4. 3/5
5. 5/3

Correct Answer: E
Solution and Explanation:
Approach Solution 1:

Important concept: x^2 is always bigger than or equal to 0.
As a result, \(-x^2\) is always less than or equal to 0
And because of this, -x^2 - 3 is always negative.
In other words, y's denominator is unquestionably NEGATIVE.

Two scenarios are possible from here:
Case I: Y is positive if the numerator of yy is negative.
Case II: If yy has a positive numerator, then y is negative.

We require a negative denominator because we want to MAXIMIZE the value of y. (which would make y POSITIVE)
But |3x - 5|, the numerator, will never be less than or equal to 0.
The only way to maximize the value of y is to make the numerator zero, as we are unable to make it negative.
To put it another way: |3x - 5|=0
It implies that 3x - 5 = 0
So
3x=5
x=5/3
E is the correct choice.

Approach Solution 2:

We have y=|3x−5| / (−x^2−3)
The denominator, −x^2−3 MUST be Negative
The Numerator, |3x−5| can NOT be Negative

i.e. y = |3x−5| / (−x^2−3) MUST be Non-Positive
i.e.. The maximum Value of a non-Positive function can be ZERO when the Numerator is Zero[

i.e. 3x-5 = 0
i.e. y is maximum at x=5/3 and ymax=0
E is the right choice.

“If y = |3x - 5|/(-x^2 - 3) for what value of x will the value of y be" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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